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Abstract

In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional derivatives are considered under some appropriate conditions, and the nonlinearity is allowed to be singular in regard to not only time variable but also space variable and it includes fractional derivatives. The existence of positive solutions for boundary conditions involving fractional derivatives is established. Finally, an example is given to demonstrate the validity of our main results.

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Curtin University would like to pay our respect to the indigenous members of our community by acknowledging the traditional owners of the land on which the Bentley Campus is located, the Wadjuk people of the Nyungar Nation; and on our Kalgoorlie Campus, the Wongutha people of the North-Eastern Goldfields.Watch our traditional Aboriginal welcome